Development and application of competing risks and multi-state models in cancer epidemiology

Abstract

Competing risks and multi-state models allow us to study complex disease settings and answer composite research questions and should be used more widely in epidemiology. This thesis aims to explore the competing risks and multi-state models areas using flexible parametric survival models (FPSMs), studying several aspects, such as the choice of timescale, choice of multi-state structure, sharing information across transitions by imposing restrictions in the estimation of the parameters, as well as communicating the results of such models to a wider audience and evaluating the use of recurrent multi-state structures in the area of recurrent events when a terminal event is present.

In competing risks settings, a common timescale is normally used for all competing events. For example, in a setting where death due to colon cancer is the event of interest and death due to other causes serves as a competing event, time since diagnosis is frequently used as the timescale when modelling the hazard rates for both events. However, attained age has been proposed as a more natural timescale when modelling mortality rate that is not associated with the event of interest (colon cancer). In Study I, the aim was to assess how the choice of timescale for other cause mortality (time since diagnosis versus attained age) influence the estimated cumulative incidence functions (CIFs) and how several factors contribute to that influence (sample size, non-proportional hazards, shape of baseline other cause mortality rate, variance in age at diagnosis) via a simulation analysis, assuming that the mortality rate is a function of attained age. I found that the bias of the CIF estimates for colon cancer mortality is negligible under all the different approaches and all factor levels. The bias in the CIF estimates for other cause mortality is also low when using time since diagnosis as the timescale for both events, provided that we include age at diagnosis in the models with sufficient flexibility (splines). When a covariate has non-proportional hazards for other cause mortality on the attained age scale, using time since diagnosis as the timescale for other cause mortality may lead to a low but non-negligible bias, no matter how flexibly we model the hazard rate.

The structural complexity of a multi-state structure and the variety of the predicted measures over time for individuals with different covariate patterns may render the communication of the results complicated and difficult. This issues motivated me to develop an interactive web- tool in Study II that can be used from researchers to present their multi-state model results to audiences with a variety of interactive graphs that will render the results more communicable and intuitive. The name of the application is MSMplus and it was written using the package RShiny in R. Multi-state model results can easily be wrapped up and uploaded to the application using the multistate package in Stata and the MSMplus package in R.

When studying a disease process, different research questions may require different multi-state structures in order to be addressed, each structure with different interpretations of the estimated measures, advantages compared to the other structures as well as limitations. There are also a number of modelling choices to consider such as the timescale used for each transition, and sharing information across transitions by imposing specific restrictions in the estimation process. In Study III, we explore different research questions via the use of a range of multi-state models of increasing complexity when dealing with registry-based repeated prescriptions of antidepressants, using the Breast Cancer Data Base Sweden 2.0 research database. I derive probability estimates that address different research questions regarding antidepressant use patterns, beginning with a single-event survival model, moving to a competing risks and a 3- state Illness-Death model, then a 4-state unidirectional and bidirectional model with a post- medication state. Finally, I fit a multi-state structure with recurrent pairs of medication cycles/ discontinuation period states, first with separately estimated transition intensity rates and then allowing sharing of information across transitions by imposing specific restrictions between the baseline transition intensity rates.

When we are interested in studying a recurrent event process in the presence of a terminal event, there is a variety of different frameworks and approaches, joint frailty models being a framework that is frequently used. A multi-state model with recurrent event states and an absorbing state representing the terminal event can also be used in this context. In Study IV, I am interested in evaluating via simulation the use of a multi-state model with recurrent states and a competing terminal absorbing state, with and without restrictions among the baseline transition intensity rates, when the underlying data generating mechanism follows a joint frailty model. I focus on the probabilities of death and of a new recurrent event across follow-up time given zero, one, two or three previous recurrences up to the first year of the follow-up, probability measures that can be targeted by both a joint frailty and a multi-state model. Then the bias and relative precision of the different modelling approaches are evaluated. Finally, I engage in a discussion of the similarities, the different assumptions and the focus of each framework.